There is currently a host of speculation surrounding the right-back's future, as his contract with Liverpool is due to expire next summer, and it is understood that an agreement with the Reds is still some way off.
It has recently been suggested that Real Madrid have cooled their interest, with the club believing that Alexander-Arnold would ultimately come to an agreement with the Reds over a new long-term contract.
However, according to The Athletic, that is not the case, with Carlo Ancelotti's side making the England international their 'priority target' when it comes to the right-back position.
The 26-year-old, as it stands, would be free to enter into talks with Real Madrid in January over a pre-contract, with Liverpool therefore facing a race against the clock to sign him to a new deal.
Real Madrid 'make Alexander-Arnold a priority target'
Alexander-Arnold has been in the Liverpool first team since 2016, representing the club on 319 occasions in all competitions, scoring 19 goals and registering 83 assists in the process.
There remain question marks over his defensive qualities at the highest level, but he has proven himself to be one of the best attacking full-backs in world football in recent seasons.
Real Madrid have handed Dani Carvajal a new contract until June 2026, but the Spaniard is out for the remainder of the season with a serious knee injury, and he faces a battle to be ready for the start of the 2025-26 campaign.
Liverpool will continue to work to sign Alexander-Arnold to a new deal, but Real Madrid are a very difficult club to turn down, with a move to Bernabeu on a free transfer thought to be a serious possibility for the full-back.
Which other right-backs are on Real Madrid's radar?
Tottenham Hotspur's Pedro Porro is currently being linked with a move to Real Madrid, while Bayer Leverkusen's Jeremie Frimpong and Sevilla's Juanlu Sanchez are also allegedly being monitored.
A recent report claimed that Monaco's Vanderson is also on the club's radar, with the Brazilian potentially providing the best value for money, as it is believed that he could be available for as little as €20m (£16.7m) during next summer's market.
For now, with Carvajal on the sidelines, Lucas Vazquez will be filling in at right-back, with Eder Militao also an option, although Los Blancos are already short in the middle of their defence.
Ancelotti's side are said to be working to sign a new centre-back during the January transfer window, with their top target in that area of the field believed to be Al-Nassr's Aymeric Laporte.